2.2.15: Leo Tolstoy (1828-1910)
The Death of Ivan Ilyich Russian Realism This Russian writer was born in a privileged class and chose to abandon his privilege for a simple life. Beloved for the radical transformation in his work and in his life, he has become one of the most famous writers in literature. His writing reflects his life, in fact, in its simplicity and realism. As a young man in school, Tolstoy excelled in linguistics, and he master several languages. When he traveled through Europe, therefore, he was able to absorb the political and social climate through conversations with the common people he met. At home in Russia, Tolstoy sympathized with the serfs, who bore the brunt of fierce poverty brought about by war and famine. His experience in the Crimean War led to his great novel War and Peace (1869), a realistic and gruesome account of battle. Another of his great novels, Anna Karenina (1873-77), introduces the audience to the reality of relationship among corrupt human beings. Tolstoy continually treats realism as a means of admonishing others to moral righteousness. In his mid-50's, Tolstoy experienced a religious conversion that led to his abandoning the Russian Orthodox Church in favor of the simple faith and a purer form of Christianity. Instead of living in his estate house, he lived and worked alongside the peasants, worshipping with them instead of observing religious ritual. Of course, he was consequently excommunicated from the Orthodox Church. His change of lifestyle, however, endeared him to a wide audience in both Russia and Europe. He professed a religious system in which human beings are born pure, but are eventually and inevitably corrupted by society. His characters search for happiness in social success, but they only find peace in an objective and realistic acceptance of life. Tolstoy also became interested in educational theory; subsequently, he opened a school in his family manor house for the children of the country peasants who worked the land. He taught a method of inspiration that influenced educators in Europe and America, who modeled Tolstoy's approach to learning in the early stages of public educational. Tolstoy's The Death of Ivan Ilyich (1886) demonstrates the self-centeredness and shallowness of people in high society. Ilyich makes all the right moves to gain wealth and social acceptance: he marries a well-connected woman he does not really love; he neglects his wife and children in favor of his career; and, as a judge, he treats the prisoners in his court with disdain and indifference. When Ilyich must come to terms with the reality of death, he learns that the only comfort he receives is from a servant who represents the naturalness of the common people. Consider while reading:
- Describe Ivan Ilyich's wife's reaction to his illness and death.
- Describe his associates' reactions to his death.
- What is the significance of the black bag?
- How does Ilyich finally let go of life and embrace death?
Written by Karen Dodson


2.11: Observations of the Heavens- Galileo
Italian astronomer and physicist Galileo Galilei first used the telescope astronomically in 1609. He was the first to see such wonders as sunspots, which he described as blemishes on the Sun, and features on the Moon like Mare —seas or bodies of water.
Galileo’s observations of the planets were monumental.
- Mercury and Venus showed phases , which meant Mercury and Venus orbits the Sun between Earth and the Sun
-
Four bright moons around Jupiter
- Galileo’s continued observation of Jupiter’s moons was important in the Geocentric-Heliocentric Solar System debate.
- Milky Way and found it had countless stars
An interesting note about Galileo…
Galileo also worked on several problems in physics, in addition to his pioneering astronomical observations. He was a deeply religious man, as his daughter who was a nun. Galileo was held on house arrest by the Church and made to recant his theory of a Heliocentric Sun-centered Solar System. Galileo’s right hand middle finger was removed after his death and is on display in the Science Museum of Florence, along with some of his telescopes.


15.3: Customer Service
- Define customer service
cus·tom·er serv·ice
noun: customer service; plural noun: customer services
- the assistance and advice provided by a company to those people who buy or use its products or services.
Depending on who you ask, the definition of customer service varies widely depending on the understanding of the basic terms “customer” and “service.” A quick Internet search reveals thousands of interpretations of this ubiquitous business terminology. For example, the American Marketing Association defines customer service as ” a customer-oriented corporate philosophy that integrates and manages all of the elements of the customer interface within a predetermined cost-service mix .” Meanwhile, the National Retail Federation often describes customer service as something that’s not a skill but rather the result of learning and applying a combination of skills including planning, problem-solving, decision-making, critical thinking, and professionalism. [1]
Luxury automotive retailer Carl Sewell wrote in his bestselling book, Customers for Life: How to Turn That One-Time Buyer Into a Lifetime Customer , that customer service is simply asking what customers want and giving it to them.
Regardless of the definition, customer service is dependent on the act of meeting (and hopefully exceeding) the wants and needs of customers.
-
CUSTOMER SERVICE 2 24 CUSTOMER SERVICE AND SALES FUNDAMENTALS nrf.com/foundation.
↵
Contributors and Attributions
- Customer Service. Authored by : Wade Hyde. Provided by : Lumen Learning. License : CC BY: Attribution


2.13: Approval Voting
Up until now, we’ve been considering voting methods that require ranking of candidates on a preference ballot. There is another method of voting that can be more appropriate in some decision making scenarios. With Approval Voting, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.
A group of friends is trying to decide upon a movie to watch. Three choices are provided, and each person is asked to mark with an “X” which movies they are willing to watch. The results are:
\(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline & \text { Bob } & \text { Ann } & \text { Marv } & \text { Alice } & \text { Eve } & \text { Omar } & \text { Lupe } & \text { Dave } & \text { Tish } & \text { Jim } \\
\hline \text { Titanic } & & \mathrm{X} & \mathrm{X} & & & \mathrm{X} & & \mathrm{X} & & \mathrm{X} \\
\hline \text { Scream } & \mathrm{X} & & \mathrm{X} & \mathrm{X} & & \mathrm{X} & \mathrm{X} & & \mathrm{X} & \\
\hline \text { The Matrix } & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & & \mathrm{X} & & & \mathrm{X} \\
\hline
\end{array}\)
Solution
Totaling the results, we find
Titanic received 5 approvals
Scream received 6 approvals
The Matrix received 7 approvals.
In this vote, The Matrix would be the winner.
Our mathematicians deciding on a conference location from earlier decide to use Approval voting. Their votes are tallied below. Find the winner using Approval voting.
\(\begin{array}{|l|l|l|l|l|l|l|l|}
\hline & 30 & 10 & 15 & 20 & 15 & 5 & 5 \\
\hline \text { Seattle } & \mathrm{X} & \mathrm{X} & \mathrm{X} & & & \mathrm{X} & \\
\hline \text { Tacoma } & \mathrm{X} & & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & \\
\hline \text { Puyallup } & & \mathrm{X} & & \mathrm{X} & \mathrm{X} & \mathrm{X} & \\
\hline \text { Olympia } & & & \mathrm{X} & & \mathrm{X} & & \mathrm{X} \\
\hline
\end{array}\)
- Answer
-
Using Approval voting:
Seattle has \(30+10+15+5 = 60\) approval votes
Tacoma has \(30+15+20+15+5 = 85\) approval votes
Puyallup has \(10+20+25+5 = 50\) approval votes
Olympia has \(15+15+5 = 35\) approval votes


13.5: Wave Optics
Electron microscopes can make images of individual atoms, but why will a visible-light microscope never be able to? Stereo speakers create the illusion of music that comes from a band arranged in your living room, but why doesn't the stereo illusion work with bass notes? Why are computer chip manufacturers investing billions of dollars in equipment to etch chips with x-rays instead of visible light?
The answers to all of these questions have to do with the subject of wave optics. So far this book has discussed the interaction of light waves with matter, and its practical applications to optical devices like mirrors, but we have used the ray model of light almost exclusively. Hardly ever have we explicitly made use of the fact that light is an electromagnetic wave. We were able to get away with the simple ray model because the chunks of matter we were discussing, such as lenses and mirrors, were thousands of times larger than a wavelength of light. We now turn to phenomena and devices that can only be understood using the wave model of light.
12.5.1 Diffraction
Figure Figure \(\PageIndex{1a}\) shows a typical problem in wave optics, enacted with water waves. It may seem surprising that we don't get a simple pattern like Figure \(\PageIndex{1b}\), but the pattern would only be that simple if the wavelength was hundreds of times shorter than the distance between the gaps in the barrier and the widths of the gaps.
Figure \(\PageIndex{1}\) : a. In this view from overhead, a straight, sinusoidal water wave encounters a barrier with two gaps in it. Strong wave vibration occurs at angles X and Z, but there is none at all at angle Y. (The figure has been retouched from a real photo of water waves. In reality, the waves beyond the barrier would be much weaker than the ones before it, and they would therefore be difficult to see.) b / This doesn't happen.
Wave optics is a broad subject, but this example will help us to pick out a reasonable set of restrictions to make things more manageable:
- We restrict ourselves to cases in which a wave travels through a uniform medium, encounters a certain area in which the medium has different properties, and then emerges on the other side into a second uniform region.
- We assume that the incoming wave is a nice tidy sine-wave pattern with wavefronts that are lines (or, in three dimensions, planes).
- In Figure \(\PageIndex{1a}\) we can see that the wave pattern immediately beyond the barrier is rather complex, but farther on it sorts itself out into a set of wedges separated by gaps in which the water is still. We will restrict ourselves to studying the simpler wave patterns that occur farther away, so that the main question of interest is how intense the outgoing wave is at a given angle.
The kind of phenomenon described by restriction (1) is called diffraction . Diffraction can be defined as the behavior of a wave when it encounters an obstacle or a nonuniformity in its medium. In general, diffraction causes a wave to bend around obstacles and make patterns of strong and weak waves radiating out beyond the obstacle. Understanding diffraction is the central problem of wave optics. If you understand diffraction, even the subset of diffraction problems that fall within restrictions (2) and (3), the rest of wave optics is icing on the cake.
Diffraction can be used to find the structure of an unknown diffracting object: even if the object is too small to study with ordinary imaging, it may be possible to work backward from the diffraction pattern to learn about the object. The structure of a crystal, for example, can be determined from its x-ray diffraction pattern.
Diffraction can also be a bad thing. In a telescope, for example, light waves are diffracted by all the parts of the instrument. This will cause the image of a star to appear fuzzy even when the focus has been adjusted correctly. By understanding diffraction, one can learn how a telescope must be designed in order to reduce this problem --- essentially, it should have the biggest possible diameter.
There are two ways in which restriction (2) might commonly be violated. First, the light might be a mixture of wavelengths. If we simply want to observe a diffraction pattern or to use diffraction as a technique for studying the object doing the diffracting (e.g., if the object is too small to see with a microscope), then we can pass the light through a colored filter before diffracting it.
A second issue is that light from sources such as the sun or a lightbulb does not consist of a nice neat plane wave, except over very small regions of space. Different parts of the wave are out of step with each other, and the wave is referred to as incoherent . One way of dealing with this is shown in Figure \(\PageIndex{2}\). After filtering to select a certain wavelength of red light, we pass the light through a small pinhole. The region of the light that is intercepted by the pinhole is so small that one part of it is not out of step with another. Beyond the pinhole, light spreads out in a spherical wave; this is analogous to what happens when you speak into one end of a paper towel roll and the sound waves spread out in all directions from the other end. By the time the spherical wave gets to the double slit it has spread out and reduced its curvature, so that we can now think of it as a simple plane wave.
If this seems laborious, you may be relieved to know that modern technology gives us an easier way to produce a single-wavelength, coherent beam of light: the laser.
The parts of the final image on the screen in Figure \(\PageIndex{2}\) are called diffraction fringes . The center of each fringe is a point of maximum brightness, and halfway between two fringes is a minimum.
Exercise \(\PageIndex{1}\): Discussion Question
Why would x-rays rather than visible light be used to find the structure of a crystal? Sound waves are used to make images of fetuses in the womb. What would influence the choice of wavelength
12.5.2 Scaling of diffraction
This chapter has “optics” in its title, so it is nominally about light, but we started out with an example involving water waves. Water waves are certainly easier to visualize, but is this a legitimate comparison? In fact the analogy works quite well, despite the fact that a light wave has a wavelength about a million times shorter. This is because diffraction effects scale uniformly. That is, if we enlarge or reduce the whole diffraction situation by the same factor, including both the wavelengths and the sizes of the obstacles the wave encounters, the result is still a valid solution.
This is unusually simple behavior! In subsection 0.2.2 we saw many examples of more complex scaling, such as the impossibility of bacteria the size of dogs, or the need for an elephant to eliminate heat through its ears because of its small surface-to-volume ratio, whereas a tiny shrew's life-style centers around conserving its body heat.
Of course water waves and light waves differ in many ways, not just in scale, but the general facts you will learn about diffraction are applicable to all waves. In some ways it might have been more appropriate to insert this chapter after section 6.2 on bounded waves, but many of the important applications are to light waves, and you would probably have found these much more difficult without any background in optics.
Another way of stating the simple scaling behavior of diffraction is that the diffraction angles we get depend only on the unitless ratio \(\lambda \)/d, where \(\lambda\) is the wavelength of the wave and \(d\) is some dimension of the diffracting objects, e.g., the center-to-center spacing between the slits in figure a. If, for instance, we scale up both \(\lambda \) and \(d\) by a factor of 37, the ratio \(\lambda /d\) will be unchanged.
12.5.3 The Correspondence Principle
The only reason we don't usually notice diffraction of light in everyday life is that we don't normally deal with objects that are comparable in size to a wavelength of visible light, which is about a millionth of a meter. Does this mean that wave optics contradicts ray optics, or that wave optics sometimes gives wrong results? No. If you hold three fingers out in the sunlight and cast a shadow with them, either wave optics or ray optics can be used to predict the straightforward result: a shadow pattern with two bright lines where the light has gone through the gaps between your fingers. Wave optics is a more general theory than ray optics, so in any case where ray optics is valid, the two theories will agree. This is an example of a general idea enunciated by the physicist Niels Bohr, called the correspondence principle: when flaws in a physical theory lead to the creation of a new and more general theory, the new theory must still agree with the old theory within its more restricted area of applicability. After all, a theory is only created as a way of describing experimental observations. If the original theory had not worked in any cases at all, it would never have become accepted.
In the case of optics, the correspondence principle tells us that when \(\lambda /d\) is small, both the ray and the wave model of light must give approximately the same result. Suppose you spread your fingers and cast a shadow with them using a coherent light source. The quantity \(\lambda /d\) is about \(10^{-4}\), so the two models will agree very closely. (To be specific, the shadows of your fingers will be outlined by a series of light and dark fringes, but the angle subtended by a fringe will be on the order of \(10^{-4}\) radians, so they will be invisible and washed out by the natural fuzziness of the edges of sun-shadows, caused by the finite size of the sun.)
Exercise \(\PageIndex{1}\)
What kind of wavelength would an electromagnetic wave have to have in order to diffract dramatically around your body? Does this contradict the correspondence principle?
- Answer
-
(answer in the back of the PDF version of the book)
12.5.4 Huygens' Principle
Returning to the example of double-slit diffraction, f, note the strong visual impression of two overlapping sets of concentric semicircles. This is an example of Huygens' principle , named after a Dutch physicist and astronomer. (The first syllable rhymes with “boy.”) Huygens' principle states that any wavefront can be broken down into many small side-by-side wave peaks, g, which then spread out as circular ripples, h, and by the principle of superposition, the result of adding up these sets of ripples must give the same result as allowing the wave to propagate forward, i.
In the case of sound or light waves, which propagate in three dimensions, the “ripples” are actually spherical rather than circular, but we can often imagine things in two dimensions for simplicity.
In double-slit diffraction the application of Huygens' principle is visually convincing: it is as though all the sets of ripples have been blocked except for two. It is a rather surprising mathematical fact, however, that Huygens' principle gives the right result in the case of an unobstructed linear wave, h and i. A theoretically infinite number of circular wave patterns somehow conspire to add together and produce the simple linear wave motion with which we are familiar.
Since Huygens' principle is equivalent to the principle of superposition, and superposition is a property of waves, what Huygens had created was essentially the first wave theory of light. However, he imagined light as a series of pulses, like hand claps, rather than as a sinusoidal wave.
The history is interesting. Isaac Newton loved the atomic theory of matter so much that he searched enthusiastically for evidence that light was also made of tiny particles. The paths of his light particles would correspond to rays in our description; the only significant difference between a ray model and a particle model of light would occur if one could isolate individual particles and show that light had a “graininess” to it. Newton never did this, so although he thought of his model as a particle model, it is more accurate to say he was one of the builders of the ray model.
Almost all that was known about reflection and refraction of light could be interpreted equally well in terms of a particle model or a wave model, but Newton had one reason for strongly opposing Huygens' wave theory. Newton knew that waves exhibited diffraction, but diffraction of light is difficult to observe, so Newton believed that light did not exhibit diffraction, and therefore must not be a wave. Although Newton's criticisms were fair enough, the debate also took on the overtones of a nationalistic dispute between England and continental Europe, fueled by English resentment over Leibniz's supposed plagiarism of Newton's calculus. Newton wrote a book on optics, and his prestige and political prominence tended to discourage questioning of his model.
Thomas Young (1773-1829) was the person who finally, a hundred years later, did a careful search for wave interference effects with light and analyzed the results correctly. He observed double-slit diffraction of light as well as a variety of other diffraction effects, all of which showed that light exhibited wave interference effects, and that the wavelengths of visible light waves were extremely short. The crowning achievement was the demonstration by the experimentalist Heinrich Hertz and the theorist James Clerk Maxwell that light was an electromagnetic wave. Maxwell is said to have related his discovery to his wife one starry evening and told her that she was the only other person in the world who knew what starlight was.
12.5.5 Double-slit diffraction
Let's now analyze double-slit diffraction, k, using Huygens' principle. The most interesting question is how to compute the angles such as X and Z where the wave intensity is at a maximum, and the in-between angles like Y where it is minimized. Let's measure all our angles with respect to the vertical center line of the figure, which was the original direction of propagation of the wave.
If we assume that the width of the slits is small (on the order of the wavelength of the wave or less), then we can imagine only a single set of Huygens ripples spreading out from each one, l. White lines represent peaks, black ones troughs. The only dimension of the diffracting slits that has any effect on the geometric pattern of the overlapping ripples is then the center-to-center distance, \(d\), between the slits.
We know from our discussion of the scaling of diffraction that there must be some equation that relates an angle like \(\theta_Z\) to the ratio \(\lambda /d\),
If the equation for \(\theta_Z\) depended on some other expression such as \(\lambda +d\) or \(\lambda^2/d\), then it would change when we scaled \(\lambda \) and \(d\) by the same factor, which would violate what we know about the scaling of diffraction.
Along the central maximum line, X, we always have positive waves coinciding with positive ones and negative waves coinciding with negative ones. (I have arbitrarily chosen to take a snapshot of the pattern at a moment when the waves emerging from the slit are experiencing a positive peak.) The superposition of the two sets of ripples therefore results in a doubling of the wave amplitude along this line. There is constructive interference. This is easy to explain, because by symmetry, each wave has had to travel an equal number of wavelengths to get from its slit to the center line, m: Because both sets of ripples have ten wavelengths to cover in order to reach the point along direction X, they will be in step when they get there.
At the point along direction Y shown in the same figure, one wave has traveled ten wavelengths, and is therefore at a positive extreme, but the other has traveled only nine and a half wavelengths, so it at a negative extreme. There is perfect cancellation, so points along this line experience no wave motion.
But the distance traveled does not have to be equal in order to get constructive interference. At the point along direction Z, one wave has gone nine wavelengths and the other ten. They are both at a positive extreme.
self-check:
At a point half a wavelength below the point marked along direction X, carry out a similar analysis.
(answer in the back of the PDF version of the book)
To summarize, we will have perfect constructive interference at any point where the distance to one slit differs from the distance to the other slit by an integer number of wavelengths. Perfect destructive interference will occur when the number of wavelengths of path length difference equals an integer plus a half.
Now we are ready to find the equation that predicts the angles of the maxima and minima. The waves travel different distances to get to the same point in space, n. We need to find whether the waves are in phase (in step) or out of phase at this point in order to predict whether there will be constructive interference, destructive interference, or something in between.
One of our basic assumptions in this chapter is that we will only be dealing with the diffracted wave in regions very far away from the object that diffracts it, so the triangle is long and skinny. Most real-world examples with diffraction of light, in fact, would have triangles with even skinner proportions than this one. The two long sides are therefore very nearly parallel, and we are justified in drawing the right triangle shown in figure o, labeling one leg of the right triangle as the difference in path length , \(L-L'\), and labeling the acute angle as \(\theta \). (In reality this angle is a tiny bit greater than the one labeled \(\theta \) in figure n.)
The difference in path length is related to \(d\) and \(\theta \) by the equation
Constructive interference will result in a maximum at angles for which \(L-L'\) is an integer number of wavelengths,
Here \(m\) equals 0 for the central maximum, \(-1\) for the first maximum to its left, \(+2\) for the second maximum on the right, etc. Putting all the ingredients together, we find \(m\lambda/d=\sin \theta \), or
Similarly, the condition for a minimum is
That is, the minima are about halfway between the maxima.
As expected based on scaling, this equation relates angles to the unitless ratio \(\lambda /d\). Alternatively, we could say that we have proven the scaling property in the special case of double-slit diffraction. It was inevitable that the result would have these scaling properties, since the whole proof was geometric, and would have been equally valid when enlarged or reduced on a photocopying machine!
Counterintuitively, this means that a diffracting object with smaller dimensions produces a bigger diffraction pattern, p.
| Example 12: Double-slit diffraction of blue and red light |
|---|
|
Blue light has a shorter wavelength than red. For a given double-slit spacing \(d\), the smaller value of \(\lambda /d\) for leads to smaller values of \(\sin \theta \), and therefore to a more closely spaced set of diffraction fringes, q
|
| Example 13: The correspondence principle |
|---|
|
Let's also consider how the equations for double-slit diffraction relate to the correspondence principle. When the ratio \(\lambda /d\) is very small, we should recover the case of simple ray optics. Now if \(\lambda /d\) is small, \(\sin\theta \) must be small as well, and the spacing between the diffraction fringes will be small as well. Although we have not proven it, the central fringe is always the brightest, and the fringes get dimmer and dimmer as we go farther from it. For small values of \(\lambda /d\), the part of the diffraction pattern that is bright enough to be detectable covers only a small range of angles. This is exactly what we would expect from ray optics: the rays passing through the two slits would remain parallel, and would continue moving in the \(\theta =0\) direction. (In fact there would be images of the two separate slits on the screen, but our analysis was all in terms of angles, so we should not expect it to address the issue of whether there is structure within a set of rays that are all traveling in the \(\theta =0\) direction.) |
| Example 14: Spacing of the fringes at small angles |
|---|
|
At small angles, we can use the approximation \(\sin\theta\approx\theta\), which is valid if \(\theta \) is measured in radians. The equation for double-slit diffraction becomes simply
\[\begin{equation*} \frac{\lambda}{d} = \frac{\theta}{m} , \end{equation*}\]
which can be solved for \(\theta \) to give
\[\begin{equation*} \theta = \frac{m\lambda}{d} . \end{equation*}\]
The difference in angle between successive fringes is the change in \(\theta \) that results from changing \(m\) by plus or minus one,
\[\begin{equation*} \Delta\theta = \frac{\lambda}{d} . \end{equation*}\]
For example, if we write \(\theta_7\) for the angle of the seventh bright fringe on one side of the central maximum and \(\theta_8\) for the neighboring one, we have
\[\begin{align*} \theta_8-\theta_7 &= \frac{8\lambda}{d}-\frac{7\lambda}{d}\\ &= \frac{\lambda}{d} , \end{align*}\]
and similarly for any other neighboring pair of fringes. |
Although the equation \(\lambda /d=\sin \theta /m\) is only valid for a double slit, it is can still be a guide to our thinking even if we are observing diffraction of light by a virus or a flea's leg: it is always true that
(1) large values of \(\lambda /d\) lead to a broad diffraction pattern, and
(2) diffraction patterns are repetitive.
In many cases the equation looks just like \(\lambda /d =\sin \theta /m\) but with an extra numerical factor thrown in, and with \(d\) interpreted as some other dimension of the object, e.g., the diameter of a piece of wire.
12.5.6 Repetition
Suppose we replace a double slit with a triple slit, s. We can think of this as a third repetition of the structures that were present in the double slit. Will this device be an improvement over the double slit for any practical reasons?
The answer is yes, as can be shown using figure u. For ease of visualization, I have violated our usual rule of only considering points very far from the diffracting object. The scale of the drawing is such that a wavelengths is one cm. In u/1, all three waves travel an integer number of wavelengths to reach the same point, so there is a bright central spot, as we would expect from our experience with the double slit. In figure u/2, we show the path lengths to a new point. This point is farther from slit A by a quarter of a wavelength, and correspondingly closer to slit C. The distance from slit B has hardly changed at all. Because the paths lengths traveled from slits A and C differ by half a wavelength, there will be perfect destructive interference between these two waves. There is still some uncanceled wave intensity because of slit B, but the amplitude will be three times less than in figure u/1, resulting in a factor of 9 decrease in brightness. Thus, by moving off to the right a little, we have gone from the bright central maximum to a point that is quite dark.
Now let's compare with what would have happened if slit C had been covered, creating a plain old double slit. The waves coming from slits A and B would have been out of phase by 0.23 wavelengths, but this would not have caused very severe interference. The point in figure u/2 would have been quite brightly lit up.
To summarize, we have found that adding a third slit narrows down the central fringe dramatically. The same is true for all the other fringes as well, and since the same amount of energy is concentrated in narrower diffraction fringes, each fringe is brighter and easier to see, t.
This is an example of a more general fact about diffraction: if some feature of the diffracting object is repeated, the locations of the maxima and minima are unchanged, but they become narrower.
Taking this reasoning to its logical conclusion, a diffracting object with thousands of slits would produce extremely narrow fringes. Such an object is called a diffraction grating.
12.5.7 Single-slit diffraction
If we use only a single slit, is there diffraction? If the slit is not wide compared to a wavelength of light, then we can approximate its behavior by using only a single set of Huygens ripples. There are no other sets of ripples to add to it, so there are no constructive or destructive interference effects, and no maxima or minima. The result will be a uniform spherical wave of light spreading out in all directions, like what we would expect from a tiny lightbulb. We could call this a diffraction pattern, but it is a completely featureless one, and it could not be used, for instance, to determine the wavelength of the light, as other diffraction patterns could.
All of this, however, assumes that the slit is narrow compared to a wavelength of light. If, on the other hand, the slit is broader, there will indeed be interference among the sets of ripples spreading out from various points along the opening. Figure v shows an example with water waves, and figure w with light.
self-check:
How does the wavelength of the waves compare with the width of the slit in figure v?
(answer in the back of the PDF version of the book)
We will not go into the details of the analysis of single-slit diffraction, but let us see how its properties can be related to the general things we've learned about diffraction. We know based on scaling arguments that the angular sizes of features in the diffraction pattern must be related to the wavelength and the width, \(a\), of the slit by some relationship of the form
This is indeed true, and for instance the angle between the maximum of the central fringe and the maximum of the next fringe on one side equals \(1.5\lambda/a\). Scaling arguments will never produce factors such as the 1.5, but they tell us that the answer must involve \(\lambda /a\), so all the familiar qualitative facts are true. For instance, shorter-wavelength light will produce a more closely spaced diffraction pattern.
An important scientific example of single-slit diffraction is in telescopes. Images of individual stars, as in figure y, are a good way to examine diffraction effects, because all stars except the sun are so far away that no telescope, even at the highest magnification, can image their disks or surface features. Thus any features of a star's image must be due purely to optical effects such as diffraction. A prominent cross appears around the brightest star, and dimmer ones surround the dimmer stars. Something like this is seen in most telescope photos, and indicates that inside the tube of the telescope there were two perpendicular struts or supports. Light diffracted around these struts. You might think that diffraction could be eliminated entirely by getting rid of all obstructions in the tube, but the circles around the stars are diffraction effects arising from single-slit diffraction at the mouth of the telescope's tube! (Actually we have not even talked about diffraction through a circular opening, but the idea is the same.) Since the angular sizes of the diffracted images depend on \(\lambda \)/a, the only way to improve the resolution of the images is to increase the diameter, \(a\), of the tube. This is one of the main reasons (in addition to light-gathering power) why the best telescopes must be very large in diameter.
self-check:
What would this imply about radio telescopes as compared with visible-light telescopes?
(answer in the back of the PDF version of the book)
Double-slit diffraction is easier to understand conceptually than single-slit diffraction, but if you do a double-slit diffraction experiment in real life, you are likely to encounter a complicated pattern like figure aa/1, rather than the simpler one, 2, you were expecting. This is because the slits are fairly big compared to the wavelength of the light being used. We really have two different distances in our pair of slits: \(d\), the distance between the slits, and \(w\), the width of each slit. Remember that smaller distances on the object the light diffracts around correspond to larger features of the diffraction pattern. The pattern 1 thus has two spacings in it: a short spacing corresponding to the large distance \(d\), and a long spacing that relates to the small dimension \(w\).
Discussion Question
◊ Why is it optically impossible for bacteria to evolve eyes that use visible light to form images?
The principle of least time
In subsection 12.1.5 and 12.4.5, we saw how in the ray model of light, both refraction and reflection can be described in an elegant and beautiful way by a single principle, the principle of least time. We can now justify the principle of least time based on the wave model of light. Consider an example involving reflection, ab. Starting at point A, Huygens' principle for waves tells us that we can think of the wave as spreading out in all directions. Suppose we imagine all the possible ways that a ray could travel from A to B. We show this by drawing 25 possible paths, of which the central one is the shortest. Since the principle of least time connects the wave model to the ray model, we should expect to get the most accurate results when the wavelength is much shorter than the distances involved --- for the sake of this numerical example, let's say that a wavelength is 1/10 of the shortest reflected path from A to B. The table, 2, shows the distances traveled by the 25 rays.
Note how similar are the distances traveled by the group of 7 rays, indicated with a bracket, that come closest to obeying the principle of least time. If we think of each one as a wave, then all 7 are again nearly in phase at point B. However, the rays that are farther from satisfying the principle of least time show more rapidly changing distances; on reuniting at point B, their phases are a random jumble, and they will very nearly cancel each other out. Thus, almost none of the wave energy delivered to point B goes by these longer paths. Physically we find, for instance, that a wave pulse emitted at A is observed at B after a time interval corresponding very nearly to the shortest possible path, and the pulse is not very “smeared out” when it gets there. The shorter the wavelength compared to the dimensions of the figure, the more accurate these approximate statements become.
Instead of drawing a finite number of rays, such 25, what happens if we think of the angle, \(\theta \), of emission of the ray as a continuously varying variable? Minimizing the distance \(L\) requires
Because \(L\) is changing slowly in the vicinity of the angle that satisfies the principle of least time, all the rays that come out close to this angle have very nearly the same \(L\), and remain very nearly in phase when they reach B. This is the basic reason why the discrete table, ab/2, turned out to have a group of rays that all traveled nearly the same distance.
As discussed in subsection 12.1.5, the principle of least time is really a principle of least or greatest time. This makes perfect sense, since \(dL/d \theta =0\) can in general describe either a minimum or a maximum
The principle of least time is very general. It does not apply just to refraction and reflection --- it can even be used to prove that light rays travel in a straight line through empty space, without taking detours! This general approach to wave motion was used by Richard Feynman, one of the pioneers who in the 1950's reconciled quantum mechanics with relativity. A very readable explanation is given in a book Feynman wrote for laypeople, QED: The Strange Theory of Light and Matter.
Contributors and Attributions
- Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.


6.11: Introduction to Probability Rules
What you’ll learn to do: Reason from probability distributions, using probability rules, to answer probability questions.
In this section, we introduce probability rules and properties. These rules can make evaluating probabilities far simpler and can also help catch mistakes if results are nonsensical (for example, a 140% chance is impossible). We revisit conditional probabilities, which are a fundamental concept in understanding how to interpret results from hypothesis testing. Finally, we introduce the notion of independence, joint, and marginal probabilities, and present a useful rule that ties these concepts together.
Contributors and Attributions
CC licensed content, Shared previously
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


16.2: Period and Frequency in Oscillations
Learning Objectives
By the end of this section, you will be able to:
- Observe the vibrations of a guitar string.
- Determine the frequency of oscillations.
When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time. Each successive vibration of the string takes the same time as the previous one. We define periodic motion to be a motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by an object on a spring moving up and down. The time to complete one oscillation remains constant and is called the period \(T\). Its units are usually seconds, but may be any convenient unit of time. The word period refers to the time for some event whether repetitive or not; but we shall be primarily interested in periodic motion, which is by definition repetitive. A concept closely related to period is the frequency of an event.
For example, if you get a paycheck twice a month, the frequency of payment is two per month and the period between checks is half a month. Frequency \(f\) is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is
\[f = \dfrac{1}{T},\]
The SI unit for frequency is the cycle per second , which is defined to be a hertz (Hz):
\[1 \, Hz = 1 \dfrac{cycle}{sec} \, or 1 \, Hz = \dfrac{1}{s}\]
A cycle is one complete oscillation. Note that a vibration can be a single or multiple event, whereas oscillations are usually repetitive for a significant number of cycles.
Example \(\PageIndex{1}\): Determine the Frequency of Two Oscillations, Medical Ultrasound and the Period of Middle C
We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let’s try one example of each.
- A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs. What is the frequency of this oscillation?
- The frequency of middle C on a typical musical instrument is 264 Hz. What is the time for one complete oscillation?
Strategy
Both questions (a) and (b) can be answered using the relationship between period and frequency. In question (a), the period \(T\) is given and we are asked to find frequency \(f\). In question (b), the frequency is given and we are asked to find the period \(T\).
Solution a
Substitute 0.400 \(\mu s\) for \(T\) in \(f = \dfrac{1}{T}\):
\[f = \dfrac{1}{T} = \dfrac{1}{0.400 \times 10^{-6} s}.\]
Solve to find
\[f = 2.50 \times 10^6 \, Hz.\]
Discussion a
The frequency of sound found in (a) is much higher than the highest frequency that humans can hear and, therefore, is called ultrasound. Appropriate oscillations at this frequency generate ultrasound used for noninvasive medical diagnoses, such as observations of a fetus in the womb.
Solution b
-
Identify the known values:
The time for one complete oscillation is the period \(T\): \[f = \dfrac{1}{T}.\]
- Solve for \(T\): \[T = \dfrac{1}{f}.\]
- Substitute the given value for the frequency into the resulting expression: \[T = \dfrac{1}{f} = \dfrac{1}{264 \, Hz} = \dfrac{1}{264 \, cycles/s} = 3.79 \times 10^{-3} s = 3.79 \, ms.\]
Discussion
The period found in (b) is the time per cycle, but this value is often quoted as simply the time in convenient units (ms or milliseconds in this case).
Exercise \(\PageIndex{1}\)
Identify an event in your life (such as receiving a paycheck) that occurs regularly. Identify both the period and frequency of this event.
- Answer
-
I visit my parents for dinner every other Sunday. The frequency of my visits is 26 per calendar year. The period is two weeks.
Summary
- Periodic motion is a repetitious oscillation.
- The time for one oscillation is the period \(T\).
- The number of oscillations per unit time is the frequency \(f\).
- These quantities are related by \(f = \dfrac{1}{T}.\)
Glossary
- period
- time it takes to complete one oscillation
- periodic motion
- motion that repeats itself at regular time intervals
- frequency
- number of events per unit of time


7.3: Presenting Quantitative Data Graphically
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Quantitative, or numerical, data can also be summarized into frequency tables.
Example 9
A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:
19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0
These scores could be summarized into a frequency table by grouping like values:
\(\begin{array}{|c|c|}
\hline \textbf { Score } & \textbf { Frequency } \\
\hline 0 & 2 \\
\hline 5 & 1 \\
\hline 12 & 1 \\
\hline 15 & 2 \\
\hline 16 & 2 \\
\hline 17 & 4 \\
\hline 18 & 8 \\
\hline 19 & 4 \\
\hline 20 & 6 \\
\hline
\end{array}\)
Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data:
However, since the scores are numerical values, this chart doesn’t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a histogram .
Histogram
A histogram is like a bar graph, but where the horizontal axis is a number line
Example 10
For the values above, a histogram would look like:
Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at ½ values to avoid this ambiguity.
Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.
If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .
Class Intervals
Class intervals are groupings of the data. In general, we define class intervals so that:
- Each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
- We have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.
Example 11
Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.
\(\begin{array}{|c|c|}
\hline \textbf { Interval } & \textbf { Frequency } \\
\hline 120-134 & 4 \\
\hline 135-149 & 14 \\
\hline 150-164 & 16 \\
\hline 165-179 & 28 \\
\hline 180-194 & 12 \\
\hline 195-209 & 8 \\
\hline 210-224 & 7 \\
\hline 225-239 & 6 \\
\hline 240-254 & 2 \\
\hline 255-269 & 3 \\
\hline
\end{array}\)
A histogram of this data would look like:
In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.
Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.
Try it Now 3
The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.
$140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285
$285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320
$330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460
- Answer
-
Using a class intervals of size 55, we can group our data into six intervals:
\(\begin{array}{|l|r|}
\hline \textbf { cost interval } & \textbf { Frequency } \\
\hline \$ 140-194 & 5 \\
\hline \$ 195-249 & 3 \\
\hline \$ 250-304 & 9 \\
\hline \$ 305-359 & 12 \\
\hline \$ 360-414 & 4 \\
\hline \$ 415-469 & 3 \\
\hline
\end{array}\)We can use the frequency distribution to generate the histogram.
When collecting data to compare two groups, it is desirable to create a graph that compares quantities.
Example 12
The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.
\(\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\textbf { Interval } \\
\textbf { (milliseconds) }
\end{array} & \begin{array}{c}
\textbf { Frequency } \\
\textbf { small target }
\end{array} & \begin{array}{c}
\textbf { Frequency } \\
\textbf { large target }
\end{array} \\
\hline 300-399 & 0 & 0 \\
\hline 400-499 & 1 & 5 \\
\hline 500-599 & 3 & 10 \\
\hline 600-699 & 6 & 5 \\
\hline 700-799 & 5 & 0 \\
\hline 800-899 & 4 & 0 \\
\hline 900-999 & 0 & 0 \\
\hline 1000-1099 & 1 & 0 \\
\hline 1100-1199 & 0 & 0 \\
\hline
\end{array}\)
One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.
Frequency polygon
An alternative representation is a frequency polygon . A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.
Example 13
This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.


10.6.8: The Sex,Gender,Sexuality System
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- Miliann Kang, Donovan Lessard, Laura Heston, and Sonny Nordmarken
- University of Massachusetts Amherst via UMass Amherst Libraries
- Miliann Kang, Donovan Lessard, Laura Heston, and Sonny Nordmarken
- University of Massachusett Amherst
The phrase “ sex/gender system, ” or “ sex/gender/sexuality system ” was coined by Gayle Rubin (1984) to describe, “the set of arrangements by which a society transforms biological sexuality into products of human activity.” That is, Rubin proposed that the links between biological sex, social gender, and sexual attraction are products of culture. Gender is, in this case, “the social product” that we attach to notions of biological sex. In our heteronormative culture, everyone is assumed to be heterosexual (attracted to men if you are a woman; attracted to women if you are a man) until stated otherwise.  Rubin questioned the biological determinist argument that suggested all people assigned female at birth will identify as women and be attracted to men. According to a biological determinist view, where “biology is destiny,” this is the way nature intended. However, this view fails to account for human intervention. As human beings, we have an impact on the social arrangements of society. Social constructionists believe that many things we typically leave unquestioned as conventional ways of life actually reflect historically- and culturally-rooted power relationships between groups of people, which are reproduced in part through socialization processes, where we learn conventional ways of thinking and behaving from our families and communities. Just because female-assigned people bear children does not necessarily mean that they are always by definition the best caretakers of those children or that they have “natural instincts” that male-assigned people lack.
For instance, the arrangement of women caring for children has a historical legacy (which we will discuss more in the section on gendered labor markets). We see not only mothers but other women too caring for children: daycare workers, nannies, elementary school teachers, and babysitters. What these jobs have in common is that they are all very female-dominated occupations AND that this work is economically undervalued. These people do not get paid very well. One study found that, in New York City, parking lot attendants, on average, make more money than childcare workers (Clawson and Gerstel, 2002). Because “mothering” is not seen as work, but as a woman’s “natural” behavior, she is not compensated in a way that reflects how difficult the work is. If you have ever babysat for a full day, go ahead and multiply that by eighteen years and then try to make the argument that it is not work. Men can do this work just as well as women, but there are no similar cultural dictates that say they should. On top of that, some suggest that if paid caretakers were mostly men, then they would make much more money. In fact, men working in female-dominated occupations actually earn more and gain promotions faster than women. This phenomenon is referred to as the glass escalator. This example illustrates how, as social constructionist Abby Ferber (2009) argues, social systems produce differences between men and women, and not the reverse.


3.8: Case Questions
In 2017, it became apparent that Wells Fargo had created over 2 million falsified customer accounts without the customers’ consent, approval, or knowledge. John Stumpf, Wells Fargo CEO, who resigned amid this scandal, denied any leadership involvement and wrongdoing. He blamed his employees and fired over 5,300 employees over this scandal. Research this case and answer the following questions.
- What organizational and company-culture factors convinced employees to create false accounts?
- Why did the employees not question leadership?
In 2017, the US Environmental Protection Agency found that Volkswagen had installed a “defeat device”—software in the vehicle that detects that an emissions test is in progress, controls the engine, reduces emissions, and enables the vehicle to pass the test for US emissions standards. Martin Winterkorn, CEO of Volkswagen, denied any wrongdoing, was later forced to resign, and admitted they had cheated. Research this case and answer the following questions.
- What organizational and cultural factors convinced Volkswagen employees to cheat?
- Why did the workforce not question leadership?
If you were to create a top-ten list of the world’s greatest corruption scandals, the problems of Petrobras ( Petróleo Brasileiro ) in Brazil surely would make the list. The majority state-owned petroleum conglomerate was a party to a multibillion-dollar scandal in which company executives received bribes and kickbacks from contractors in exchange for lucrative construction and drilling contracts. The contractors paid Petrobras executives upward of 5 percent of the contract amount, which was funneled back into slush funds. The slush funds, in turn, paid for the election campaigns of certain members of the ruling political party, Partido dos Trabalhadores , or the Workers Party, as well as for luxury items like race cars, jewelry, Rolex watches, yachts, wine, and art. 30 The original investigation into these practices was known as Operation Car Wash ( Lava Jato ) and began in 2014 at a gas station and car wash in Brasília, where money was being laundered. It has since expanded to include scrutiny of senators, government officials, and the former president of the republic, Luiz Inácio Lula da Silva. The probe also contributed to the impeachment and removal of Lula’s successor, Dilma Rousseff. Lula and Rousseff are members of the Workers Party. The case is complex, revealing Chinese suppliers, Swiss bank accounts where money was hidden from Brazilian authorities, and wire transfers that went through New York City and caught the eye of the US Department of Justice. In early 2017, the Brazilian Supreme Court justice in charge of the investigation and prosecution was mysteriously killed in a plane crash. It is hard to imagine a more tragic example of systemic breakdown and individual vice. The loss of trust in government and the economy still affects ordinary Brazilians. Meanwhile, the investigation continues.
- Is this Brazilian company scandal unique to that culture?
In the fall of 2016, Samsung Electronics experienced a massive public relations disaster when its Galaxy Note 7 smartphones started exploding due to faulty batteries and casings. Initially, the company denied there were any technical problems. Then, when it became obvious the exploding phones posed a safety and health threat (they were banned from airplanes), Samsung accused its suppliers of creating the problem. In reality, the rush to beat Apple’s iPhone 7 release date was the most likely reason corners were cut in production. Samsung finally owned up to the problem, recalled more than two million phones worldwide, and replaced them with new, improved Galaxy Note 7s. The company’s response and its replacement of the phones went a long way toward defusing the disaster and even boosting the company’s share price. Samsung focused on the customer (i.e., customer safety and satisfaction) with the motive of doing the ethically responsible thing.
- Although some might argue the company could have done far more and much more quickly, perhaps it still acted reasonably. What do you think?
Sometimes engaged employees go above and beyond in the interest of customer service, even if they have no “customers” to speak of. Kathy Fryman is one such employee. Fryman was a custodian for three decades at a 100-year-old school in the Augusta (KY) Independent School District. She was not just taking care of the school building, she was also taking care of the people inside. 61 Fryman fixed doors that would not close, phones that would not ring, and alarms that did not sound when they should. She kept track of keys and swept up dirty floors before parents’ night. That was all part of the job of custodian, but she did much more. Fryman would often ask the nurse how an ill student was doing. She would check with a teacher about a kid who was going through tough times at home. If a teacher mentioned needing something, the next day it would show up on his or her desk. A student who needed something for class would suddenly find it in his or her backpack. Speaking of Fryman, district superintendent Lisa McCrane said, “She just has a unique way of making others feel nurtured, comforted, and cared for.” According to Fryman, “…I need to be doing something for somebody.” Fryman’s customers were not there to buy a product on which she would make a commission. Her customers were students and teachers, parents and taxpayers. Yet she provided the kind of service that all employers would be proud of, the kind that makes a difference to people every day.
- Is there a way for a manager to find, develop, and encourage the next Fryman, or is the desire to “do something good for somebody” an inherent trait in some employees that is missing in others?
- Employees who display Fryman’s zeal often do so for their own internal rewards. Others may simply want to be recognized and appreciated for their effort. If you were the superintendent in her district, how would you recognize Fryman? Could she, for example, be invited to speak to new hires about opportunities to render exceptional service?
Please view the video ABC Nightline-IDEO Shopping Cart on YouTube. This video demonstrates how an entrepreneurial mindset combined along with a collaborative process can be used to deliver the most innovative products.
- After watching the IDEO YouTube video, list the different factors that has enabled IDEO to become an industry example for corporate innovation.
- What top principles and behaviors that has contributed to the development of a culture of collaborative excellence?


6.3: Overview of Managerial Decision-Making
- Understand the basic characteristics of decision making.
Decision-making is the action or process of thinking through possible options and selecting one.
It is important to recognize that managers are continually making decisions and that the quality of their decision-making has an impact—sometimes quite significant—on the effectiveness of the organization and its stakeholders. Stakeholders are all the individuals or groups that are affected by an organization (such as customers, employees, shareholders, etc.).
Members of the top management team regularly make decisions that affect the future of the organization and all its stakeholders, such as deciding whether to pursue a new technology or product line. A good decision can enable the organization to thrive and survive long-term, while a poor decision can lead a business into bankruptcy. Managers at lower levels of the organization generally have a smaller impact on the organization’s survival but can still have a tremendous impact on their department and its workers. Consider, for example, a first-line supervisor who is charged with scheduling workers and ordering raw materials for her department. Poor decision-making by lower-level managers is unlikely to drive the entire firm out of existence, but it can lead to many adverse outcomes, such as:
- reduced productivity if there are too few workers or insufficient supplies,
- increased expenses if there are too many workers or too many supplies, particularly if the supplies have a limited shelf life or are costly to store, and
- frustration among employees, reduced morale, and increased turnover (which can be costly for the organization) if the decisions involve managing and training workers.
Deciding When to Decide
While some decisions are simple, a manager’s decisions are often complex ones that involve a range of options and uncertain outcomes. When deciding among various options and uncertain outcomes, managers need to gather information, which leads them to another necessary decision: how much information is needed to make a good decision? Managers frequently make decisions without complete information; indeed, one of the hallmarks of an effective leader is the ability to determine when to hold off on a decision and gather more information and when to make a decision with the information at hand. Waiting too long to make a decision can be as harmful to the organization as reaching a decision too quickly. Failing to react quickly enough can lead to missed opportunities, yet acting too quickly can lead to organizational resources being poorly allocated to projects with no chance of success. Effective managers must decide when they have gathered enough information and must be prepared to change course if additional information becomes available that makes it clear that the original decision was a poor one. For individuals with fragile egos, changing course can be challenging because admitting to a mistake can be harder than forging ahead with a bad plan. Effective managers recognize that given the complexity of many tasks, some failures are inevitable. They also realize that it’s better to minimize a bad decision’s impact on the organization and its stakeholders by recognizing it quickly and correcting it.
What’s the Right (Correct) Answer?
It’s also worth noting that making decisions as a manager is not at all like taking a multiple-choice test: with a multiple-choice test, there is always one right answer. This is rarely the case with management decisions. Sometimes a manager is choosing between multiple good options, and it’s not clear which will be the best. Other times there are multiple bad options, and the task is to minimize harm. Often there are individuals in the organization with competing interests, and the manager must make decisions knowing that someone will be upset no matter what decision is reached.
What’s the Right (Ethical) Answer?
Sometimes managers are asked to make decisions that go beyond just upsetting someone—they may be asked to make decisions in which harm could be caused to others. These decisions have ethical or moral implications. Ethics and morals refer to our beliefs about what is right vs. wrong, good vs. evil, virtuous vs. corrupt. Implicitly, ethics and morals relate to our interactions with and impact on others—if we never had to interact with another creature, we would not have to think about how our behaviors affected other individuals or groups. All managers, however, make decisions that impact others. It is, therefore, important to be mindful about whether our decisions have a positive or a negative impact. “Maximizing shareholder wealth” is often used as a rationalization for placing the importance of short-term profits over the needs of others who will be affected by a decision—such as employees, customers, or local citizens (who might be affected, for example, by environmental decisions). Maximizing shareholder wealth is often a short-sighted decision, however, because it can harm the organization’s financial viability in the future.1 Bad publicity, customers boycotting the organization, and government fines are all possible long-term outcomes when managers make choices that cause harm in order to maximize shareholder wealth. More importantly, increasing the wealth of shareholders is not an acceptable reason for causing harm to others.
As you can see from these brief examples, management is not for the faint of heart! It can, however, be incredibly rewarding to be in a position to make decisions that have a positive impact on an organization and its stakeholders. We see a great example of this in the Sustainability and Responsible Management box.
The focus of a manager or a business owner is often primarily on doing well (making a profit). Sometimes, though, organizational leaders choose to pursue two big goals at once: doing well and simultaneously doing good (benefiting society in some way). Why? Generally, because they think it’s an important thing to do. The business provides an opportunity to pursue another goal that the founders, owners, or managers are also passionate about. In the case of New Belgium Brewing, the company’s co-founders, Jeff Lebesch and Kim Jordan, were passionate about two things: making great beer and environmental stewardship. So it should come as no surprise that their brewery is dedicated to reducing its environmental footprint. The brewery has created a culture that fosters sustainability in a wide range of ways, such as by giving employees a bicycle on their one-year anniversary as a way to encourage them to ride bicycles to work. The organization is also active in advocacy efforts, such as the “Save the Colorado” (river) campaign, and it works hard to promote responsible decision-making when it comes to environmental issues. In fact, in 1999, following an employee vote, the brewery began to purchase all of its electricity from wind power, even though it was more expensive than electricity from coal-burning power plants (which meant reduced profitability and less money for employee bonuses).
While the brewery still relies primarily on wind power, it also now generates a portion of its electricity onsite—some from rooftop solar panels and even more from biogas, the methane gas byproduct that is created by microbes in the brewery’s water treatment plant. The company cleans the wastewater generated from beer production, and in doing so, it generates biogas, which is captured and used for energy to help run the brewery.
Brewing is water intensive, so New Belgium works hard to reduce water consumption and to recycle the water that it does use. The company also reduces other types of waste by selling used grain, hops, and yeast to local ranchers for cattle feed. The company, which has been employee-owned since 2013, also works with the local utility through a Smart Meter program to reduce their energy consumption at peak times.
All of these efforts at doing good must come at a cost, right? Actually, research shows that companies that are committed to sustainability have superior financial performance, on average, relative to those that are not. In coming up with creative ways to reduce, reuse, and recycle, employees often also find ways to save money (like using biogas). In addition, organizations that strive to do good are often considered attractive and desirable places to work (especially by people who have similar values) and are also valued by the surrounding communities. As a result, employees in those organizations tend to be extremely committed to them, with high levels of engagement, motivation, and productivity. Indeed, it seems clear that the employees at the New Belgium Brewery are passionate about where they work and what they do. This passion generates value for the organization and proves that it is, in fact, possible to do well while having also made the decision to do good. And in the case of New Belgium Brewery, that means working to protect the environment while also making delicious beer.
Discussion Questions
- What challenges does New Belgium Brewery face in pursuing environmental goals?
- Can you think of any other examples of companies that try to “do good” while also doing well?
- Would you like to work for an organization that is committed to something more than just profitability, even if it meant your salary or bonus would be smaller?
Sources:
Crofton, K. (2014). “How New Belgium Brewery leads Colorado’s craft brewers in energy,” GreenBiz, https://www.greenbiz.com/ .
Dahl, D. (2016). “How New Belgium Brewing Has Found Sustainable Success,” Forbes, https://www.forbes.com/ .
Foust, J. (2016). “New Belgium Brewing Once Again Named Platinum-Level Bicycle Friendly Business by the League of American Bicyclists,” Craft Beer.com.
Eccles, R., Ioannou, I., & Serafeim, G. (2014). “The Impact of Corporate Sustainability on Organizational Processes and Performance,” Management Science, 60, doi.org/10.1287/mnsc.2014.1984.
New Belgium Brewery Sustainability. (2017). www.newbelgium.com/sustainability.
- What are some positive outcomes of decision-making for an organization? What are some possible negative outcomes?
- How is managerial decision-making different from a multiple-choice test?
- In addition to the owners of a business, who are some of the other stakeholders that managers should consider when making decisions?